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Some limit behaviors for the LS estimator in simple linear EV regression models

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  • Miao, Yu
  • Wang, Ke
  • Zhao, Fangfang

Abstract

In the present paper, we study the simple linear errors in variables (EV) model: [eta]i=[theta]+[beta]xi+[epsilon]i,[xi]i=xi+[delta]i, with i.i.d. errors . The consistency and asymptotic normality for the LS estimators and of the unknown parameters [beta],[theta] are obtained, which weaken some known conditions and improve some known results. Finally, the large deviation principle for and are given under the assumptions that ([epsilon]i,[delta]i) possess normal distributions.

Suggested Citation

  • Miao, Yu & Wang, Ke & Zhao, Fangfang, 2011. "Some limit behaviors for the LS estimator in simple linear EV regression models," Statistics & Probability Letters, Elsevier, vol. 81(1), pages 92-102, January.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:1:p:92-102
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    References listed on IDEAS

    as
    1. Deaton, Angus, 1985. "Panel data from time series of cross-sections," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 109-126.
    2. Gao, Fuqing, 2001. "Moderate deviations for the maximum likelihood estimator," Statistics & Probability Letters, Elsevier, vol. 55(4), pages 345-352, December.
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    Cited by:

    1. Yu Miao & Fangfang Zhao & Ke Wang & Yanping Chen, 2013. "Asymptotic normality and strong consistency of LS estimators in the EV regression model with NA errors," Statistical Papers, Springer, vol. 54(1), pages 193-206, February.
    2. Yi Wu & Xuejun Wang & Shuhe Hu & Lianqiang Yang, 2018. "Weighted version of strong law of large numbers for a class of random variables and its applications," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(2), pages 379-406, June.
    3. Xuejun Wang & Yi Wu & Shuhe Hu, 2018. "Strong and weak consistency of LS estimators in the EV regression model with negatively superadditive-dependent errors," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 102(1), pages 41-65, January.
    4. Yi Wu & Xuejun Wang & Aiting Shen, 2023. "Strong Convergence for Weighted Sums of Widely Orthant Dependent Random Variables and Applications," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-28, March.
    5. Xuejun Wang & Aiting Shen & Zhiyong Chen & Shuhe Hu, 2015. "Complete convergence for weighted sums of NSD random variables and its application in the EV regression model," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(1), pages 166-184, March.
    6. Di Hu & Pingyan Chen & Soo Hak Sung, 2017. "Strong laws for weighted sums of $$\psi $$ ψ -mixing random variables and applications in errors-in-variables regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(3), pages 600-617, September.
    7. Yan Wang & Xuejun Wang, 2021. "Complete f-moment convergence for Sung’s type weighted sums and its application to the EV regression models," Statistical Papers, Springer, vol. 62(2), pages 769-793, April.

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